Tomosynthetic image reconstruction method, and diagnostic device operating according to the method

ABSTRACT

In a tomosynthetic image reconstruction method and diagnostic device operating with such a method, a tomosynthetic 3D x-ray image is reconstructed by a discrete filtered back projection from a number of individual digital projection data recorded from different project angles within a restricted angular range, in which at least one filtering is performed with a convolution kernel that, in the local area outside of its central value, corresponds to an exponential function.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a tomosynthetic image reconstruction method,especially suitable for mammography, in which a tomosynthetic 3D x-rayimage is assembled from individual digital images recorded from a numberof different projection angles. In addition the invention relates to adiagnostic device operating with such a method.

2. Description of the Prior Art

Mammography involves x-ray examination of the female breast for thepurpose of detecting tumors at the earliest possible stage. Byconstantly improving mammography methods an attempt is made to generatex-ray images supplying a high level of information, in order todistinguish beneficial from harmful changes and to reduce the number ofincorrect findings, i.e. the number of suspicious findings that arecaused by non-harmful changes, and the number of the undiscoveredharmful tumors. In conventional x-ray mammography in this case atwo-dimensional single image of the compressed breast is produced in asingle projection direction. Since in such a projection the tissuelayers lying behind each other in the direction of the x-ray beam areoverlaid, heavily-absorbent beneficial structures can overlay a harmfultumor and render such detectability more difficult.

To avoid this, mammography methods known as tomosynthesis are known fromDobbins J T, III, Godfrey D J. “Digital x-ray tomosynthesis: currentstate of the art and clinical potential”, Physics in Medicine andBiology 48, R65-R106, 2003, in which individual images of the femalebreast or projection data can be recorded in a number of differentprojection directions with a digital x-ray detector. From theseindividual digital images recorded from different projection angles,i.e. from the image data belonging to these individual images, athree-dimensional image data set, for example composed of a number oflayer images, that each represent one layer of the breast oriented inparallel to the reception surface of the x-ray detector, can begenerated by image reconstruction methods. Such an image data setobtained by reconstruction is referred to below as a tomosynthetic 3Dx-ray image. This technique enables tissue structures at a lower depthin the direction of propagation of the x-ray beam to be better detected.

Because of the incomplete scanning, i.e. the projections are onlyavailable from a restricted angular range, a reconstruction of a 3Dx-ray image is only possible to a limited extent, so that the imagequality of a tomosynthetic 3D x-ray image does not achieve the imagequality known from computed tomography (CT). Thus, for example, theresolution in the direction of the central beam, referred to as thedepth resolution, is reduced compared to the resolution in the layers atright angles to this. Also because of the incomplete scanning noquantitative values of the attenuation coefficient μ can bereconstructed, so that the character or impression of the image obtainedwith tomosynthesis also differs from the character of an image obtainedwith computer tomography methods. The imaging task on such cases focusesmore in obtaining the best possible three-dimensional visualization ofthe object under the given projection conditions than on a quantitativereconstruction of the local absorption coefficient μ.

In tomography as well as in tomosynthesis the diagnostic evaluationcapability of a reconstructed 3D x-ray image is heavily dependent of thereconstruction algorithms used, which in addition must be optimized withrespect to the respective diagnostic problem.

The reconstruction methods known in the prior art for tomosynthesis arefor example summarized in the aforementioned article by Dobbins et al.Essentially the methods employ unfiltered back projection (Niklason L T,Christian B T, Niklason L E, et al., “Digital Tomosynthesis in BreastImaging”, Radiology 205, 399-406, 1997), non-linear back projection(Suryanarayanan S, Karellas A, Vedantham S, et al., “Evaluation ofLinear and Nonlinear Tomosynthetic Reconstruction Methods in DigitalMammography”, Academic Radiology 8, 219-224, 2001), matrix inversionmethods (D. J. Godfrey, A. Rader and J. T. Dobbins, III, “PracticalStrategies for the Clinical Implementation of Matrix InversionTomosynthesis (MITS), Medical Imaging 2003: Physics of Medical Imaging,Proc. SPIE Vol. 5030 (2003), pp. 379-389), iterative (algebraic) methods(Wu T, Stewart A, Stanton M, et al., “Tomographic Mammography Using aLimited Number of Low-dose Cone-beam Projection Images”, Medical Physics30, 365-380, 2003; Wu T, Moore R, Rafferty E A, Kopans D B, “AComparison of Reconstruction Algorithms for Breast Tomosynthesis”,Medical Physics 31, 2636-2647, 2004), and filtered back projection (FBP)(Wu T, Moore R. Rafferty E A, Kopans D B, “A Comparison ofReconstruction Algorithms for Breast Tomosynthesis”, Medical Physics 31,2636-2647, 2004; Lauritsch G, Haerer W H, “A Theoretical Framework forFiltered Backprojection in Tomosynthesis”, Proc. SPIE, 3338, 1127-1137,1998 and U.S. Pat. No. 6,442,288).

With filtered back projection the measurement data provided by the x-raydetectors is filtered and subsequently projected back onto a volumematrix—the digital three-dimensional image of a part volume of theobject. It is one of the most promising reconstruction methods since itis based on an analytical algorithm that can be obtained from thescanning geometry and is numerically very efficient and stable.Previously such methods have essentially used filters which are similarto the filters used in tomographic reconstruction. Thus, in theaforementioned article by Wu et al, for example, a filtered backprojection specifically developed by Feldkamp for tomography on orbitalpaths using a cone-shaped x-ray beam bundle and known as the Feldkampalgorithm Feldkamp et al is applied.

Because of the basically incomplete nature of a tomosyntheticreconstruction in mammography, reconstruction algorithms, as are knownfrom tomography, cannot simply be used for tomosynthetic reconstructionwithout any problems.

SUMMARY OF THE INVENTION

An object of the invention is to provide a tomosynthesis imagereconstruction method, especially for mammography, with which, usingminimal processing effort, a 3D x-ray image can be generated that can beevaluated diagnostically in the best possible manner. An object of theinvention is also to provide a diagnostic device operatable with such animage reconstruction method.

The first object is achieved in accordance with the invention by animage reconstruction method wherein a tomosynthetic 3D x-ray image isreconstructed by a filtered back projection from a number of individualdigital images recorded at different position angles in a restrictedangular range, in which filtering is undertaken with a discreteconvolution kernel which in the local area outside zero corresponds toan exponential function.

A discrete convolution or filtering is defined by the relationship

${{y(n)} = {\sum\limits_{k = {- \infty}}^{k = {+ \infty}}\; {{h(k)}{x\left( {n - k} \right)}}}},$

with h(k) being the so-called convolution kernel, x(n) the sequence ofthe measurement or image data—the intensities of the x-radiationmeasured in various discrete channels at various discrete angularpositions—and y(n) is the series of filtered data generated by theconvolution. The inventive discrete convolution kernel—referred to belowas the exponential core—is defined in the spatial domain by thefollowing relationship:

h(0) (central value, for k→∝h(0)=1) applies

h(1)=−(1−a)/2

h(k)=h(1)a ^(k-1)

and

h(k)=h(−k) for k<0

In such cases k is an integer with |k|>1 and corresponds to the spatialvariable in parallel to the receiver surface, expressed in units of aspatial distance, for example the distance between two adjacent channelsof the x-ray detector, with which, for the discrete inventiveconvolution or filtering—designated below as exponentialfiltering—summation is executed instead of an integration.

The parameter “a” can be used to control the character of the image tobe reconstructed with regard to contrast, local sharpness and noisebehavior. Preferably “a” lies between the values of zero and one. In thelimit case of a=0 the convolution kernel corresponds to a Laplacefilter, with which only one reconstruction of edges in the image isundertaken (X or λ reconstruction). In the limit case of a=1 the unitycore is produced, with which the so-called layergram, i.e. the simpleback projection, can be reconstructed.

The filtering can be undertaken both in the spatial domain and also inthe frequency domain. To this end the Fourier transforms of themeasurement or image data are multiplied by the Fourier transforms ofthe exponential core and this product is subsequently Fourierback-transformed. Such a procedure, which mathematically leads to thesame result produces a simplification of the mathematical operationsrequired and thus speeds up the image reconstruction.

The exponential filtering alternatively can be performed afterwards atdata record level on a data record already filtered with another filter,or at image level on a 3D image created with another reconstructionmethod from this data.

The use of such a convolution kernel (exponential core) corresponding toan exponential function is known for tomography from U.S. Pat. No.6,125,136, the disclosure of which is incorporated herein by reference.The invention is based on the insight that this known reconstructionmethod is especially suitable for image reconstruction with incompleteimage data sets, as are present in tomosynthesis, since with such anexponential core even projection data available from only one smallangular area enable the structures, microcalcification or tumorsespecially relevant to diagnosis in mammography to be presented so as tobe particularly recognizable by the appropriate choice of parameter “a”.In other words, by using such an exponential filter, although the objectis not reconstructed exactly (quantitative reproduction of the objectdensity) and the emphasis is placed more on the visualization of edgeareas, this is of advantage for tomosynthesis, since such quantitativeinformation is in principle not possible because of the incompletescanning.

The image character can be set to match the problem, e.g. withaccentuation of small high-contrast structures on the one hand (forexample microcalcifications in mammography), or lower-contrast densities(tumors) on the other hand. This is achieved by the appropriate choiceof the factor a, which preferably amounts to around 0.9 for mammography.The option of recursive implementation enables the filtering to beperformed extremely quickly.

The exponential drop in the filter coefficients and where necessary theadditional shortening of the core length L means that the filter corealso decays must more quickly than in normal tomography or tomosynthesisfilters. Such short effective core lengths very effectively limit theextent to which data disturbances can propagate in the image.Particularly the problem in tomosynthesis of generally only truncatedprojections being enabled, in which the projection cone does notcompletely cover the object under examination, is significantly reduced,since with short cores the assigned image errors can no longer propagatefrom edge of the image into the interior.

For a convolution kernel h(k) limited to a finite length L it is also ofadvantage to define the central value h(0) such that the core sumbecomes equal to zero

${{\sum\limits_{k = {- \infty}}^{k = {+ \infty}}\; {h(k)}} = 0},{{{with}\mspace{14mu} L} = {{2N} + 1}}$

This is achieved by setting

${h(0)} = {\sum\limits_{k \neq 0}{{h(k)}.}}$

Such a zero sum characteristic has proved to be especially advantageousfor image quality.

In an advantageous embodiment of the invention the filtering can also beimplemented in a recursive form, as is explained in greater detail inU.S. Pat. No. 6,125,163. The result of a convolution with theexponential core defined above is also achieved if the result of anaveraged recursive filtering of the order one is subtracted from theresult A recursive filter of the order one is defined by thespecification

Y(n)=ay(n−1)+bx(n)

This can be translated into

${y(n)} = {b{\sum\limits_{i = 0}^{n - 1}\; {a^{i} \cdot {x\left( {n - i} \right)}}}}$

If u(n) is written for the ascending direction and v(n) for the resultin the failing direction, the following is obtained

${u(n)} = {b{\sum\limits_{i = 0}^{n - 1}\; {a^{i} \cdot {x\left( {n - 1} \right)}}}}$and${v(n)} = {b{\sum\limits_{i = 0}^{n - 1}\; {a^{i} \cdot {{x\left( {n - 1} \right)}.{If}}}}}$$\begin{matrix}{{W(n)} = {{c \cdot {x(n)}} - \left( {{u(n)} - {v(n)}} \right)}} \\{= {{c \cdot {x(n)}} - {2 \cdot b \cdot {x(n)}} - {b{\sum\limits_{i > 0}^{\;}\; {a^{i}\left( {{x\left( {n + i} \right)} + {x\left( {n - i} \right)}} \right)}}}}} \\{= {{\left( {c - {2b}} \right){x(n)}} - {{ba}{\sum\limits_{i > 0}^{\;}\; {a^{i - 1}\left( {{x\left( {n + i} \right)} + {x\left( {n - i} \right)}} \right)}}}}}\end{matrix}$

and C is selected as

C=h(0)−1+1/a

with h(0) as the central component of the exponential filter definedabove, as well as

${b = \frac{1 - a}{2a}},$

the result is

${W(n)} = {{{h(0)} \cdot {x(n)}} - {\frac{\left( {1 - a} \right)}{2}{\sum\limits_{i > 0}^{\;}\; {a^{i - 1}\left( {{x\left( {n + i} \right)} + {x\left( {n - i} \right)}} \right)}}}}$

That is the result of a normal convolution with the exponential filterfor the parameter a≠0. In the special case a=0 the exponential filterdoes not need to be implemented recursively since it consists of onlythree elements.

The above object also is achieved in accordance with the presentinvention by a diagnostic device for producing a tomosynthetic 3D x-rayimage using the reconstruction method in accordance with the inventiondescribed above, including the various embodiments. This device has anx-ray tube that is moveable within a restricted range relative to anexamination subject, and a digital x-ray detector that records digitalprojection data at different projection angles of the x-ray beam emittedby the x-ray tube. An evaluation device processes the detector signalsto reconstruct the tomosynthetic 3D x-ray image in accordance with oneor more embodiments of the image reconstruction method in accordancewith the invention, as described above.

DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an embodiment of a device in accordancewith the invention.

FIG. 2 is a flowchart of an embodiment of the method in accordance withthe invention.

FIGS. 3 and 4 are diagrams in which Fourier transforms, or the Fouriertransforms of an inventive exponential filter standardized to theFourier transforms of a ramp filter, are plotted against thestandardized local frequency for different parameters “a”.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

According to FIG. 1 the device, in the exemplary embodiment amammography device, has an x-ray tube 2 for generating x-rays 3 thatpass through an object under examination 4. The object under examination4 is a female breast which is held between a compression plate 6 and asupport plate 8. The x-rays passing through the object under examination4, the compression plate 6 and the support plate 8 are received by awide-area digital x-ray detector 10 which is formed by a number ofindividual detectors 12 arranged in a matrix-shaped array, and of whichthe receive surface 11 is arranged in parallel to the plates 6, 8.

The x-ray tube 2 is arranged to enable its location to be changed in arestricted area in relation to the object under examination, and can forexample within a restricted angular range φ₁,φ₂ be pivoted around anaxis M perpendicular to the recording plane into different angularpositions j=1 . . . n, so that individual images of the object underexamination 4 at different projection angles α_(j) relative to thenormal 13 of the receive surface 11 of the x-ray detector 10 can becreated. The angular range φ₁,φ₂ does not have to be arrangedsymmetrically to the normal 13 in this case. These individual images orthe projection data P_(αj) assigned to these images in each case areassembled in a control and evaluation unit 14 containing an imageprocessor by reconstruction into a tomosynthetic 3D x-ray image T anddisplayed on a monitor 18. The x-ray detector 10 does not change itslocation during the pivoting movement of the x-ray tubes 2. It is alsopossible however to pivot the x-ray detector 10 as well or to move it sothat it follows the pivoting movement of the x-ray tubes 2 in a linearmanner.

A movement of the x-ray tubes 2 on a restricted linear path instead ofthe pivoting movement is also permitted, so that the height differencebetween x-ray detector 10 and x-ray tubes remains constant. This lineartrack likewise does not have to run symmetrically to the normal 13. Withthis linear movement there is an alignment of the x-ray tubes 2 to theobject under examination 4, so that in this case as well individualimages of the object under examination 4 can be recorded from differentangles of projection α_(j) but in a restricted angular range.

The angular position j, or in the case of a linear movement, the linearposition and the alignment of the x-ray tubes 2 as well as theiroperating parameters is controlled by control signals S which aregenerated by the control and evaluation unit 14. With the aid of inputelements, shown generically in the example by a keyboard 16, differentimage reconstructions, explained below, can be selected and executed bythe user.

The sequence of the reconstruction is illustrated schematically in theflowchart shown in FIG. 2. In a first step the projection data Pαj aresubjected to preprocessing, e.g. a logarithmic scaling and anormalization. After this preprocessing the convolution or filtering isundertaken with the convolution kernel h(k) in accordance with theinvention. Subsequently, by back projection of all projections, takinginto account their recording geometry, e.g. the relevant positions offocus and detector, a volume image V is calculated. This is subjected tofurther post-processing where necessary, e.g. by means of an imageprocessing program, a filtering or by means of a CAD program(CAD=Computer-Aided-Diagnosis) to allow a software-supported diagnosis.It represents the system-driven only approximately reconstructed spatialdistribution of the x-ray absorption coefficients μ and is presentedvisually as a tomosynthetic 3D x-ray image T either on the screen of amonitor or fed to an automated, software-supported evaluation(diagnose).

The inventive convolution or filtering can also be performed as part ofpost-processing on a volume image V which has been created by unfilteredback projection or by another reconstruction algorithm instead of on theprojections.

The diagram depicted in FIG. 3 plots the Fourier transforms H(v) of theinventive exponential core h(k) for different parameters a against thelocal frequency v. The Fourier transform H(v) is normalized to itsmaximum value, the local frequency v to a limit frequency v_(g) given bylength L of the core. In the example the calculation has been performedfor an exponential core h(k) of length L=255.

The curve of what is known as the ramp filter |v| is also entered in thediagram. It can now be seen from the diagram that, the extent to whichhigh local frequencies are suppressed can be significantly influenced bythe selection of the parameter “a”.

The extent to which high local frequencies are suppressed in relation toa ramp filter |v| depending on parameter a, is especially evident in thediagram shown in FIG. 4 in which the Fourier transform H(v) of theexponential core normalized on the ramp filter |v| is plotted fordifferent parameters against the local frequency.

Although modifications and changes may be suggested by those skilled inthe art, it is the intention of the inventors to embody within thepatent warranted hereon all changes and modifications as reasonably andproperly come within the scope of their contribution to the art.

1. A tomosynthetic image reconstruction method, comprising the steps of: from a plurality of sets of digital projection data, obtained at different projection angles, within a restricted angular range, of an x-ray beam that penetrates an examination subject to produce the projection data, reconstructing a tomosynthetic 3D image with an image reconstruction procedure; and in said image reconstruction procedure, employing a discrete filtered back projection of each of said sets of digital projection data by filtering with a convolution kernel having a central value and a local area outside the central value corresponding to an exponential function.
 2. A tomosynthetic image reconstruction method as claimed in claim 1 comprising performing said filtering recursively.
 3. A tomosynthetic image reconstruction method as claimed in claim 1 comprising employing a convolution kernel that is restricted to a finite length.
 4. A tomosynthetic image reconstruction method as claimed in claim 3 comprising selecting said central value of said convolution kernel to cause a core sum to equal zero in said discrete filtered back projection.
 5. An apparatus for producing a tomosynthetic 3D x-ray image, comprising: an x-ray tube that emits an x-ray beam moveable through a restricted angular range relative to an examination subject; a digital x-ray detector disposed to detect radiation in said x-ray beam, after passing through said examination subject, at a plurality of different projection angles in said restricted range, thereby producing a plurality of sets of digital projection data respectively for said angles; and an evaluation device supplied with said plurality of sets of digital projection data, said evaluation device executing a software program to reconstruct a tomosynthetic x-ray image from said plurality of sets of digital projection data by a discrete filtered back projection wherein filtering is performed with a convolution kernel having a central value and corresponding, in a local area outside of said central value, to an exponential function,
 6. An apparatus as claimed in claim 5 wherein said evaluation unit executes said software program to perform said filtering recursively.
 7. An apparatus as claimed in claim 5 wherein said evaluation unit employs, in said software program, a convolution kernel that is restricted to a finite length.
 8. An apparatus as claimed in claim 5 wherein said evaluation unit, in said software program, selects said convolution kernel to cause a core sum of said convolution kernel to be equal to zero in said discrete filtered back projection. 